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A System of Logic -- A priori and a posteriori -- Abacus logic -- Abduction (logic) -- Abductive validation -- Academia Analitica -- Accuracy and precision -- Ad captandum -- Ad hoc hypothesis -- Ad hominem -- Affine logic -- Affirming the antecedent -- Affirming the consequent -- Algebraic logic -- Ambiguity -- Analysis -- Analysis (journal) -- Analytic reasoning -- Analytic–synthetic distinction -- Anangeon -- Anecdotal evidence -- Antecedent (logic) -- Antepredicament -- Anti-psychologism -- Antinomy -- Apophasis -- Appeal to probability -- Appeal to ridicule -- Archive for Mathematical Logic -- Arché -- Argument -- Argument by example -- Argument form -- Argument from authority -- Argument map -- Argumentation theory -- Argumentum ad baculum -- Argumentum e contrario -- Ariadne's thread (logic) -- Aristotelian logic -- Aristotle -- Association for Informal Logic and Critical Thinking -- Association for Logic, Language and Information -- Association for Symbolic Logic -- Attacking Faulty Reasoning -- Australasian Association for Logic -- Axiom -- Axiom independence -- Axiom of reducibility -- Axiomatic system -- Axiomatization --
Backward chaining -- Barcan formula -- Begging the question -- Begriffsschrift -- Belief -- Belief bias -- Belief revision -- Benson Mates -- Bertrand Russell Society -- Biconditional elimination -- Biconditional introduction -- Bivalence and related laws -- Blue and Brown Books -- Boole's syllogistic -- Boolean algebra (logic) -- Boolean algebra (structure) -- Boolean network --
Canonical form -- Canonical form (Boolean algebra) -- Cartesian circle -- Case-based reasoning -- Categorical logic -- Categories (Aristotle) -- Categories (Peirce) -- Category mistake -- Catuṣkoṭi -- Circular definition -- Circular reasoning -- Circular reference -- Circular reporting -- Circumscription (logic) -- Circumscription (taxonomy) -- Classical logic -- Clocked logic -- Cognitive bias -- Cointerpretability -- Colorless green ideas sleep furiously -- Combinational logic -- Combinatory logic -- Combs method -- Common knowledge (logic) -- Commutativity of conjunction -- Completeness (logic) -- Composition of Causes -- Compossibility -- Comprehension (logic) -- Computability logic -- Concept -- Conceptualism -- Condensed detachment -- Conditional disjunction -- Conditional probability -- Conditional proof -- Conditional quantifier -- Confirmation bias -- Conflation -- Confusion of the inverse -- Conjunction elimination -- Conjunction fallacy -- Conjunction introduction -- Conjunctive normal form -- Connexive logic -- Connotation -- Consequent -- Consistency -- Constructive dilemma -- Contra principia negantem non est disputandum -- Contradiction -- Contrapositive -- Control logic -- Conventionalism -- Converse (logic) -- Converse Barcan formula -- Correlative-based fallacies -- Counterexample -- Counterfactual conditional -- Counterintuitive -- Cratylism -- Credibility -- Criteria of truth -- Critical-Creative Thinking and Behavioral Research Laboratory -- Critical pedagogy -- Critical reading -- Critical thinking -- Critique of Pure Reason -- Curry's paradox -- Cyclic negation --
Dagfinn Føllesdal -- De Interpretatione -- De Morgan's laws -- Decidability (logic) -- Decidophobia -- Decision making -- Decisional balance sheet -- Deductive closure -- Deduction theorem -- Deductive fallacy -- Deductive reasoning -- Default logic -- Defeasible logic -- Defeasible reasoning -- Definable set -- Definist fallacy -- Definition -- Definitions of logic -- Degree of truth -- Denying the antecedent -- Denying the correlative -- Deontic logic -- Description -- Description logic -- Descriptive fallacy -- Deviant logic -- Dharmakirti -- Diagrammatic reasoning -- Dialectica -- Dialectica space -- Dialetheism -- Dichotomy -- Difference (philosophy) -- Digital timing diagram -- Dignāga -- Dilemma -- Disjunction elimination -- Disjunction introduction -- Disjunctive normal form -- Disjunctive syllogism -- Dispositional and occurrent belief -- Disquotational principle -- Dissoi logoi -- Division of Logic, Methodology, and Philosophy of Science -- Don't-care term -- Donald Davidson (philosopher) -- Double counting (fallacy) -- Double negation -- Double negative -- Double negation elimination -- Doxa -- Drinking the Kool-Aid --
EL++ -- Ecological fallacy -- Effective method -- Elimination rule -- Emotional reasoning -- Emotions in decision-making -- Empty name -- Encyclopedia of the Philosophical Sciences -- End term -- Engineered language -- Entailment -- Entitative graph -- Enumerative definition -- Epicureanism -- Epilogism -- Epistemic closure -- Equisatisfiability -- Erotetics -- Eternal statement -- Etymological fallacy -- European Summer School in Logic, Language and Information -- Evidence -- Exclusive nor -- Exclusive or -- Existential fallacy -- Existential graph -- Existential quantification -- Expert -- Explanandum -- Explanation -- Explanatory power -- Extension (semantics) -- Extensional context -- Extensional definition --
Fa (concept) -- Fact -- Fallacies of definition -- Fallacy -- Fallacy of distribution -- Fallacy of four terms -- Fallacy of quoting out of context -- Fallacy of the four terms -- False attribution -- False dilemma -- False equivalence -- False premise -- Fictionalism -- Finitary relation -- Finite model property -- First-order logic -- First-order predicate -- First-order predicate calculus -- First-order resolution -- Fitch-style calculus -- Fluidic logic -- Fluidics -- Formal fallacy -- Formal ontology -- Formal system -- Formalism (philosophy) -- Forward chaining -- Free logic -- Free variables and bound variables -- Function and Concept -- Fuzzy logic --
Game semantics -- Ganto's Ax -- Geometry of interaction -- Gilles-Gaston Granger -- Gongsun Long -- Grammaticality -- Greedy reductionism -- Grundlagen der Mathematik --
HPO formalism -- Halo effect -- Handbook of Automated Reasoning -- Hanlon's razor -- Hasty generalization -- Herbrandization -- Hetucakra -- Heyting algebra -- Higher-order predicate -- Higher-order thinking -- Historian's fallacy -- Historical fallacy -- History of logic -- History of the function concept -- Hold come what may -- Homunculus argument -- Horn clause -- Hume's fork -- Hume's principle -- Hypothetical syllogism --
Identity (philosophy) -- Identity of indiscernibles -- Idola fori -- Idola specus -- Idola theatri -- Idola tribus -- If-by-whiskey -- Iff -- Illicit major -- Illicit minor -- Illuminationism -- Immutable truth -- Imperative logic -- Implicant -- Inclusion (logic) -- Incomplete comparison -- Inconsistent comparison -- Inconsistent triad -- Independence-friendly logic -- Indian logic -- Inductive logic -- Inductive logic programming -- Inference -- Inference procedure -- Inference rule -- Inferential role semantics -- Infinitary logic -- Infinite regress -- Infinity -- Informal fallacy -- Informal logic -- Inquiry -- Inquiry (philosophy journal) -- Insolubilia -- Institute for Logic, Language and Computation -- Intellectual responsibility -- Intended interpretation -- Intension -- Intensional fallacy -- Intensional logic -- Intensional statement -- Intentional Logic -- Intermediate logic -- Interpretability -- Interpretability logic -- Interpretive discussion -- Introduction rule -- Introduction to Mathematical Philosophy -- Intuitionistic linear logic -- Intuitionistic logic -- Invalid proof -- Inventor's paradox -- Inverse (logic) -- Inverse consequences -- Irreducibility -- Is Logic Empirical? -- Isagoge -- Ivor Grattan-Guinness --
Jacobus Naveros -- Jayanta Bhatta -- Jingle-jangle fallacies -- John Corcoran (logician) -- John W. Dawson, Jr -- Journal of Applied Non-Classical Logics -- Journal of Automated Reasoning -- Journal of Logic, Language and Information -- Journal of Logic and Computation -- Journal of Mathematical Logic -- Journal of Philosophical Logic -- Journal of Symbolic Logic -- Judgment (mathematical logic) -- Judgmental language -- Just-so story --
Karnaugh map -- Kinetic logic -- Knowing and the Known -- Kripke semantics -- Kurt Gödel Society --
Language -- Language, Proof and Logic -- Lateral thinking -- Law of excluded middle -- Law of identity -- Law of non-contradiction -- Law of noncontradiction -- Law of thought -- Laws of Form -- Laws of logic -- Leap of faith -- Lemma (logic) -- Lexical definition -- Linear logic -- Linguistic and Philosophical Investigations -- Linguistics and Philosophy -- List of fallacies -- List of incomplete proofs -- List of logic journals -- List of paradoxes -- Logic -- Logic Lane -- Logic Spectacles -- Logic gate -- Logic in China -- Logic in Islamic philosophy -- Logic of class -- Logic of information -- Logic programming -- Logica Universalis -- Logica nova -- Logical Analysis and History of Philosophy -- Logical Investigations (Husserl) -- Logical Methods in Computer Science -- Logical abacus -- Logical argument -- Logical assertion -- Logical atomism -- Logical biconditional -- Logical conditional -- Logical conjunction -- Logical constant -- Logical disjunction -- Logical equality -- Logical equivalence -- Logical extreme -- Logical form -- Logical harmony -- Logical holism -- Logical NAND -- Logical NOR -- Logical operator -- Logical quality -- Logical truth -- Logicism -- Logico-linguistic modeling -- Logos -- Loosely associated statements -- Łoś–Tarski preservation theorem -- Ludic fallacy -- Lwów–Warsaw school of logic --
Main contention -- Major term -- Markov's principle -- Martin Gardner bibliography -- Masked-man fallacy -- Material conditional -- Mathematical fallacy -- Mathematical logic -- Meaning (linguistics) -- Meaning (non-linguistic) -- Meaning (philosophy of language) -- Meaningless statement -- Megarian school -- Mental model theory of reasoning -- Mereology -- Meta-communication -- Metalanguage -- Metalogic -- Metamathematics -- Metasyntactic variable -- Metatheorem -- Metavariable -- Middle term -- Minimal axioms for Boolean algebra -- Minimal logic -- Minor premise -- Miscellanea Logica -- Missing dollar riddle -- Modal fallacy -- Modal fictionalism -- Modal logic -- Model theory -- Modus ponens -- Modus tollens -- Moral reasoning -- Motivated reasoning -- Moving the goalposts -- Multigrade predicate -- Multi-valued logic -- Multiple-conclusion logic -- Mutatis mutandis -- Mutual knowledge (logic) -- Mutually exclusive events -- Münchhausen trilemma --
Naive set theory -- Name -- Narrative logic -- Natural deduction -- Natural kind -- Natural language -- Necessary and sufficient -- Necessity and sufficiency -- Negation -- Neutrality (philosophy) -- Nirvana fallacy -- Nixon diamond -- No true Scotsman -- Nominal identity -- Non-Aristotelian logic -- Non-classical logic -- Non-monotonic logic -- Non-rigid designator -- Non sequitur (logic) -- Noneism -- Nonfirstorderizability -- Nordic Journal of Philosophical Logic -- Normal form (natural deduction) -- Novum Organum -- Nyaya -- Nyāya Sūtras --
Object of the mind -- Occam's razor -- On Formally Undecidable Propositions of Principia Mathematica and Related Systems -- One-sided argument -- Ontological commitment -- Open sentence -- Opinion -- Opposing Viewpoints series -- Ordered logic -- Organon -- Original proof of Gödel's completeness theorem -- Osmund Lewry -- Ostensive definition -- Outline of logic -- Overbelief --
Package-deal fallacy -- Panlogism -- Paraconsistent logic -- Paraconsistent logics -- Parade of horribles -- Paradox -- Pars destruens/pars construens -- Pathetic fallacy -- Persuasive definition -- Peter Simons (academic) -- Philosophia Mathematica -- Philosophical logic -- Philosophy of logic -- Peirce's law -- Plural quantification -- Poisoning the well -- Polarity item -- Polish Logic -- Polish notation -- Politician's syllogism -- Polychotomous key -- Polylogism -- Polysyllogism -- Port-Royal Logic -- Possible world -- Post's lattice -- Post disputation argument -- Post hoc ergo propter hoc -- Posterior Analytics -- Practical syllogism -- Pragmatic mapping -- Pragmatic maxim -- Pragmatic theory of truth -- Pramāṇa -- Pramāṇa-samuccaya -- Precising definition -- Precision questioning -- Predicable -- Predicate (logic) -- Predicate abstraction -- Predicate logic -- Preferential entailment -- Preintuitionism -- Prescriptivity -- Presentism (historical analysis) -- Presupposition -- Principia Mathematica -- Principle of bivalence -- Principle of explosion -- Principle of nonvacuous contrast -- Principle of sufficient reason -- Principles of Mathematical Logic -- Prior Analytics -- Private Eye Project -- Pro hominem -- Probabilistic logic -- Probabilistic logic network -- Problem of future contingents -- Problem of induction -- Process of elimination -- Project Reason -- Proof-theoretic semantics -- Proof (truth) -- Proof by assertion -- Proof theory -- Propaganda techniques -- Proposition -- Propositional calculus -- Propositional function -- Propositional representation -- Propositional variable -- Prosecutor's fallacy -- Provability logic -- Proving too much -- Prudence -- Pseudophilosophy -- Psychologism -- Psychologist's fallacy --
Q.E.D. -- Quantification -- Quantization (linguistics) -- Quantum logic --
Ramism -- Rationality -- Razor (philosophy) -- Reason -- Reductio ad absurdum -- Reference -- Reflective equilibrium -- Regression fallacy -- Regular modal logic -- Reification (fallacy) -- Relativist fallacy -- Relevance -- Relevance logic -- Relevant logic -- Remarks on the Foundations of Mathematics -- Retroduction -- Retrospective determinism -- Revolutions in Mathematics -- Rhetoric -- Rigour -- Rolandas Pavilionis -- Round square copula -- Rudolf Carnap -- Rule of inference -- Rvachev function --
SEE-I -- Salva congruitate -- Salva veritate -- Satisfiability -- Scholastic logic -- School of Names -- Science of Logic -- Scientific temper -- Second-order predicate -- Segment addition postulate -- Self-reference -- Self-refuting idea -- Self-verifying theories -- Semantic theory of truth -- Semantics -- Sense and reference -- Sequent -- Sequent calculus -- Sequential logic -- Set (mathematics) -- Seven Types of Ambiguity (Empson) -- Sheffer stroke -- Ship of Theseus -- Simple non-inferential passage -- Singular term -- Situation -- Situational analysis -- Skeptic's Toolbox -- Slingshot argument -- Social software (social procedure) -- Socratic questioning -- Soku hi -- Some Remarks on Logical Form -- Sophism -- Sophistical Refutations -- Soundness -- Source credibility -- Source criticism -- Special case -- Specialization (logic) -- Speculative reason -- Spurious relationship -- Square of opposition -- State of affairs (philosophy) -- Statement (logic) -- Straight and Crooked Thinking -- Straight face test -- Straw man -- Strength (mathematical logic) -- Strict conditional -- Strict implication -- Strict logic -- Structural rule -- Studia Logica -- Studies in Logic, Grammar and Rhetoric -- Subjective logic -- Substitution (logic) -- Substructural logic -- Sufficient condition -- Sum of Logic -- Sunk costs -- Supertask -- Supervaluationism -- Supposition theory -- Survivorship bias -- Syllogism -- Syllogistic fallacy -- Symbol (formal) -- Syntactic Structures -- Syntax (logic) -- Synthese -- Systems of Logic Based on Ordinals --
T-schema -- Tacit assumption -- Tarski's undefinability theorem -- Tautology (logic) -- Temporal logic -- Temporal parts -- Teorema (journal) -- Term (argumentation) -- Term logic -- Ternary logic -- Testability -- Tetralemma -- Textual case based reasoning -- The False Subtlety of the Four Syllogistic Figures -- The Foundations of Arithmetic -- The Geography of Thought -- The Laws of Thought -- The Paradoxes of the Infinite -- Theorem -- Theoretical definition -- Theory and Decision -- Theory of justification -- Theory of obligationes -- Third-cause fallacy -- Three men make a tiger -- Tolerance (in logic) -- Topical logic -- Topics (Aristotle) -- Tractatus Logico-Philosophicus -- Train of thought -- Trairūpya -- Transferable belief model -- Transparent Intensional Logic -- TregoED -- Trikonic -- Trilemma -- Trivial objections -- Trivialism -- Truth -- Truth-bearer -- Truth condition -- Truth function -- Truth value -- Truthiness -- Truthmaker -- Type (model theory) -- Type theory -- Type–token distinction --
Ultrafinitism -- Unification (computer science) -- Unifying theories in mathematics -- Uniqueness quantification -- Universal logic -- Universal quantification -- Univocity -- Unspoken rule -- Use–mention distinction --
Vacuous truth -- Vagrant predicate -- Vagueness -- Validity -- Valuation-based system -- Van Gogh fallacy -- Venn diagram -- Vicious circle principle --
Warnier/Orr diagram -- Well-formed formula -- What the Tortoise Said to Achilles -- Willard Van Orman Quine -- William Kneale -- Window operator -- Wisdom of repugnance -- Witness (mathematics) -- Word sense --
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In logic, disjunction, also known as logical disjunction or logical or or logical addition or inclusive disjunction, is a logical connective typically notated as and read aloud as "or". For instance, the English language sentence "it is sunny or it is warm" can be represented in logic using the disjunctive formula , assuming that abbreviates "it is sunny" and abbreviates "it is warm".
First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables, so that rather than propositions such as "Socrates is a man", one can have expressions in the form "there exists x such that x is Socrates and x is a man", where "there exists" is a quantifier, while x is a variable. This distinguishes it from propositional logic, which does not use quantifiers or relations; in this sense, propositional logic is the foundation of first-order logic.
In logic, a logical connective is a logical constant. They can be used to connect logical formulas. For instance in the syntax of propositional logic, the binary connective can be used to join the two atomic formulas and , rendering the complex formula .
Propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. It deals with propositions and relations between propositions, including the construction of arguments based on them. Compound propositions are formed by connecting propositions by logical connectives. Propositions that contain no logical connectives are called atomic propositions.
In propositional logic, modus ponens, also known as modus ponendo ponens, implication elimination, or affirming the antecedent, is a deductive argument form and rule of inference. It can be summarized as "P implies Q.P is true. Therefore Q must also be true."
In logic, the semantic principleof bivalence states that every declarative sentence expressing a proposition has exactly one truth value, either true or false. A logic satisfying this principle is called a two-valued logic or bivalent logic.
A syllogism is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true.
The history of logic deals with the study of the development of the science of valid inference (logic). Formal logics developed in ancient times in India, China, and Greece. Greek methods, particularly Aristotelian logic as found in the Organon, found wide application and acceptance in Western science and mathematics for millennia. The Stoics, especially Chrysippus, began the development of predicate logic.
Deductive reasoning is the mental process of drawing deductive inferences. An inference is deductively valid if its conclusion follows logically from its premises, i.e. it is impossible for the premises to be true and the conclusion to be false.
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth, which in classical logic has only two possible values.
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. In particular, systems of intuitionistic logic do not assume the law of the excluded middle and double negation elimination, which are fundamental inference rules in classical logic.
Understood in a narrow sense, philosophical logic is the area of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. Some theorists conceive philosophical logic in a wider sense as the study of the scope and nature of logic in general. In this sense, philosophical logic can be seen as identical to the philosophy of logic, which includes additional topics like how to define logic or a discussion of the fundamental concepts of logic. The current article treats philosophical logic in the narrow sense, in which it forms one field of inquiry within the philosophy of logic.
The material conditional is an operation commonly used in logic. When the conditional symbol is interpreted as material implication, a formula is true unless is true and is false. Material implication can also be characterized inferentially by modus ponens, modus tollens, conditional proof, and classical reductio ad absurdum.
In logic, the semantics of logic or formal semantics is the study of the semantics, or interpretations, of formal and natural languages usually trying to capture the pre-theoretic notion of entailment.
"Is Logic Empirical?" is the title of two articles that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic as a consistent logical rendering of reality. The replacement derives from the work of Garrett Birkhoff and John von Neumann on quantum logic. In their work, they showed that the outcomes of quantum measurements can be represented as binary propositions and that these quantum mechanical propositions can be combined in a similar way as propositions in classical logic. However, the algebraic properties of this structure are somewhat different from those of classical propositional logic in that the principle of distributivity fails.
Giorgi Japaridze is a Georgian-American researcher in logic and theoretical computer science. He currently holds the title of Full Professor at the Computing Sciences Department of Villanova University. Japaridze is best known for his invention of computability logic, cirquent calculus, and Japaridze's polymodal logic.
Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics and to a lesser extent computer science. Logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and the study of arguments in natural language. The scope of logic can therefore be very large, ranging from core topics such as the study of fallacies and paradoxes, to specialized analyses of reasoning such as probability, correct reasoning, and arguments involving causality. One of the aims of logic is to identify the correct and incorrect inferences. Logicians study the criteria for the evaluation of arguments.
Philosophy of logic is the area of philosophy that studies the scope and nature of logic. It investigates the philosophical problems raised by logic, such as the presuppositions often implicitly at work in theories of logic and in their application. This involves questions about how logic is to be defined and how different logical systems are connected to each other. It includes the study of the nature of the fundamental concepts used by logic and the relation of logic to other disciplines. According to a common characterization, philosophical logic is the part of the philosophy of logic that studies the application of logical methods to philosophical problems, often in the form of extended logical systems like modal logic. But other theorists draw the distinction between the philosophy of logic and philosophical logic differently or not at all. Metalogic is closely related to the philosophy of logic as the discipline investigating the properties of formal logical systems, like consistency and completeness.
Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language. When used as a countable noun, the term "a logic" refers to a logical formal system that articulates a proof system. Logic plays a central role in many fields, such as philosophy, mathematics, computer science, and linguistics.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (and) denoted as ∧, disjunction (or) denoted as ∨, and the negation (not) denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction, and division. Boolean algebra is therefore a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations.
